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arXiv:1907.05990

Delayed choice experiments and causality in quantum mechanics

Dominik Šafránek

Published Jul 13, 2019• 0 citations
arXivHTMLPDF

Abstract

Although it may seem The Delayed Choice experiments contradict causality and one could construct an experiment which could possibly affect the past, using Many World interpretation we prove it is not possible. We also find a mathematical background to Which-path information and show why its obtainability prevents system from interfering. We find a system which exhibit both interference and correlation and show why one-particle interference and correlations are complementary. Better visible interference pattern leads to worse correlations and vice versa. Then, using knowledge gained from Quantum Eraser and Delayed Choice experiments we prove there is not an objective reality in a sense of Einstein, Podolsky and Rosen. Furthermore, we discuss the difference between ``outer'' (non-interacting) and ``inner'' (interacting) observer. We find the mathematical relationship between the ``universal'' wave function used by ``outer'' observer and processes the ``inner'' observer sees, which is our small contribution to the measurement problem.

DOI
10.48550/arxiv.1907.05990

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Although it may seem The Delayed Choice experiments contradict causality and one could construct an experiment which could possibly affect the past, using Many World interpretation we prove it is not possible. We also find a mathematical background to Which-path information and show why its obtainability prevents system from interfering. We find a system which exhibit both interference and correlation and show why one-particle interference and correlations are complementary. Better visible interference pattern leads to worse correlations and vice versa. Then, using knowledge gained from Quantum Eraser and Delayed Choice experiments we prove there is not an objective reality in a sense of Einstein, Podolsky and Rosen. Furthermore, we discuss the difference between outer'' (non-interacting) and inner'' (interacting) observer. We find the mathematical relationship between the universal'' wave function used by outer'' observer and processes the ``inner'' observer sees, which is our small contribution to the measurement problem.
The delayed-choice experiment and the quantum eraser experiment are two of the most challenging interpretive problems in quantum mechanics. Standard textbook accounts trace the presence or absence of interference to whether the experimenter "knows" the photon's path — a causal framework implying backward-in-time influence. This article offers an intuitive, diagram-rich account grounded in the wave-or-particle geometric framework, revealing that both experiments share a far simpler backbone: interference depends solely on how many waves reach a given detector. One wave → no interference. Two waves → interference. This conclusion alters no mathematical prediction of quantum mechanics; it merely flips the causal arrow from "knowing the path destroys interference" to "the number of waves creates interference." A forthcoming main paper will present the complete three-column correspondence (experimental step → geometry → QFT standard) with full algebraic verification.
The counterintuitive features of quantum physics challenge many common-sense assumptions. In an interferometric quantum eraser experiment, one can actively choose whether or not to erase which-path information (a particle feature) of one quantum system and thus observe its wave feature via interference or not by performing a suitable measurement on a distant quantum system entangled with it. In all experiments performed to date, this choice took place either in the past or, in some delayed-choice arrangements, in the future of the interference. Thus, in principle, physical communications between choice and interference were not excluded. Here, we report a quantum eraser experiment in which, by enforcing Einstein locality, no such communication is possible. This is achieved by independent active choices, which are space-like separated from the interference. Our setup employs hybrid path-polarization entangled photon pairs, which are distributed over an optical fiber link of 55 m in one experiment, or over a free-space link of 144 km in another. No naive realistic picture is compatible with our results because whether a quantum could be seen as showing particle- or wave-like behavior would depend on a causally disconnected choice. It is therefore suggestive to abandon such pictures altogether.
The delayed-choice quantum eraser represents an interesting experiment that exemplifies Bohr's principle of complementarity in a beautiful way. According to the complementarity principle, in a two-path interference experiment, the knowledge of which path was taken by the particle and the appearance of interference are mutually exclusive. Even when the which-path information is merely retained in specific quantum path-markers, without being actually read, it suffices to eliminate interference. Nevertheless, if this path information is erased in some manner, the interference re-emerges, a phenomenon referred to as the quantum eraser. An intriguing aspect of this experiment is that if the path information is erased after the particle has been detected on the screen, the interference still reappears, a phenomenon known as the delayed-choice quantum eraser. This observation has led to the interpretation that the particle can be influenced to exhibit characteristics of either a particle or a wave based on a decision made long after it has been registered on the screen. This idea has sparked considerable debate and discussions surrounding retrocausality. This controversy is reviewed here, and a detailed resolution provided. Quanta 2025; 14: 66–74.
This paper presents an observational analysis of the Delayed-Choice Quantum Eraser experiment through the framework of quantum mechanics. The Delayed-Choice Quantum Eraser, a variation of the classic double-slit experiment, demonstrates the intricate relationship between quantum measurement, wave-particle duality, and the temporal ordering of observations. By utilizing the principles of quantum superposition, entanglement, and the non-local collapse of the wave function, we seek to rationalize the counterintuitive outcomes observed in the experiment. Specifically, we explore how the act of measurement retroactively influences the observed behavior of particles, depending on whether or not the which-path information is available. Our analysis underscores the significance of the quantum mechanical concept of wave function collapse across spacetime, providing a deeper understanding of how quantum mechanics reconciles the delayed-choice paradox.
Abstract The delayed-choice quantum eraser has long been a subject of controversy, and has been looked at as being incomprehensible to having retro-causal effect in time. Here the delayed-choice quantum eraser is theoretically analyzed using standard quantum mechanics. Employing a Mach–Zehnder interferometer, instead of a conventional two-slit interference, brings in surprising clarity. Some common mistakes in interpreting the experiment are pointed out. It is demonstrated that in the delayed mode there is no which-way information present after the particle is registered on the screen or the final detectors, contrary to popular belief. However, it is shown that another kind of path information is present even after the particle is registered in the final detectors. The registered particle can be used to predict the results of certain yet to be made measurements on the which-way detector. This novel correlation can be tested in a careful experiment. It is consequently argued that there is no big mystery in the experiment, and no retro-causal effect whatsoever.
The principle of complementarity is one of the cornerstones of quantum theory. The aim of this study was to advance our understanding of complementarity by analyzing the role of delayed choice and quantum erasers in two-slit experiments, and by proposing experiments for verifying the analysis. The analysis is based on models consisting of measurable spaces and probability measures involved in the experiments. The main findings are as follows: (a) The complementarity principle manifests itself in such a way that wave and particle behaviors cannot be simultaneously observed almost surely with respect to any single, fixed measure. (b) Described by different measures, complementary properties can coexist in the same experimental setup. (c) Which-way information will not preclude or erase interference fringes. (d) Delayed choice and quantum erasers are irrelevant to testing complementarity. (e) It is possible for us to know through which slit each quantum object passed almost surely with respect to the measure corresponding to the slit while the interference pattern is intact. Based on the experiments analyzed, realizable experiments are proposed for verifying the above results.